Problem: Simplify the following expression: $a = \dfrac{8z^2 - 56z - 240}{z + 3} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $8$ , so we can rewrite the expression: $ a =\dfrac{8(z^2 - 7z - 30)}{z + 3} $ Then we factor the remaining polynomial: $z^2 {-7}z {-30} $ ${3} {-10} = {-7}$ ${3} \times {-10} = {-30}$ $ (z + {3}) (z {-10}) $ This gives us a factored expression: $\dfrac{8(z + {3}) (z {-10})}{z + 3}$ We can divide the numerator and denominator by $(z - 3)$ on condition that $z \neq -3$ Therefore $a = 8(z - 10); z \neq -3$